Concern nerve impulses, electrical signals propagated along...

Concern nerve impulses, electrical signals propagated along nerve fibers consisting of many axons (fiberlike extensions of nerve cells) connected end-to-end. Axons come in two varieties: insulated axons with a sheath made of myelin, and uninsulated axons with no such sheath. Myelinated (sheathed) axons conduct nerve impulses much faster than unmyelinated (unsheathed) axons. The impulse speed depends on the diameter of the axons and the sheath, but a typical myelinated axon transmits nerve impulses at a speed of about $25 \mathrm{~m} / \mathrm{s}$ much faster than the typical $2.0 \mathrm{~m} / \mathrm{s}$ for an unmyelinated axon. Figure P2.47 shows small portions of three nerve fibers consisting of axons of equal size. Two-thirds of the axons in fiber $\mathrm{B}$ are myelinated. Suppose nerve impulses simultaneously enter the left side of the nerve fibers sketched in Figure $\mathrm{P} 2.47,$ then propagate to the right. Draw qualitatively accurate position and velocity graphs for the nerve impulses in all three cases. A nerve fiber is made up of many axons, but show the propagation of the impulses only over the six axons shown here.

Concern nerve impulses, electrical signals propagated along nerve fibers consisting of many axons (fiberlike extensions of nerve cells) connected end-to-end. Axons come in two varieties: insulated axons with a sheath made of myelin, and uninsulated axons with no such sheath. Myelinated (sheathed) axons conduct nerve impulses much faster than unmyelinated (unsheathed) axons. The impulse speed depends on the diameter of the axons and the sheath, but a typical myelinated axon transmits nerve impulses at a speed of about $25 \mathrm{~m} / \mathrm{s}$ much faster than the typical $2.0 \mathrm{~m} / \mathrm{s}$ for an unmyelinated axon. Figure P2.47 shows small portions of three nerve fibers consisting of axons of equal size. Two-thirds of the axons in fiber $\mathrm{B}$ are myelinated.
Suppose nerve impulses simultaneously enter the left side of the nerve fibers sketched in Figure $\mathrm{P} 2.47,$ then propagate to the right. Draw qualitatively accurate position and velocity graphs for the nerve impulses in all three cases. A nerve fiber is made up of many axons, but show the propagation of the impulses only over the six axons shown here.

Key Concepts

Axon

Axons are long, slender projections of nerve cells that transmit electrical impulses away from the cell body. They form the basic pathways for communication within the nervous system, and their structure, including diameter, affects the speed at which impulses travel.

Myelination

Myelination is the process where axons are covered with a fatty substance called myelin, which acts as an electrical insulator. This insulation increases conduction speed by permitting saltatory conduction, where the impulse jumps between gaps in the myelin sheath.

Nerve Conduction Velocity

Nerve conduction velocity refers to the speed at which an electrical signal travels along an axon. It is influenced by factors such as axon diameter and the presence of a myelin sheath, with myelinated fibers typically exhibiting much higher conduction speeds compared to unmyelinated fibers.

Position-Time and Velocity-Time Graphs

Position-time graphs represent how the location of a nerve impulse changes over time, indicating its speed and distance traveled. Velocity-time graphs display the rate of change of position with time. Qualitative graphs of these sorts help illustrate differences in impulse propagation between fibers with differing levels of myelination.

Transcript

00:01 Okay, welcome.

00:01 So the problem i'm going to be working on today, it involves an application to biology.

00:07 What we're dealing with here is we have a question that asks us about un -milinated fibers, partially -milinated fibers, and fully -milinated fibers.

00:16 And basically, they're saying that the nerve impulses go faster down myelinated fibers.

00:23 And basically, they're going to want us to draw a position time graphs and velocities.

00:30 Time graphs for the three fibers.

00:32 So the first thing i'm going to do is give you an idea of what these fibers look like.

00:35 Now we're going to divide it into six six sections or six axons.

00:40 So for fiber a basically this is entirely unmyelinated.

00:47 So i'm just going to do that with just kind of a normal just line like this and then divide into six sections.

00:54 So there we go and there we go.

00:58 So there's six sections and these are all unmyelinated so unmyelinated and then for fiber b what we have is we have a partially myelinated fiber so what i'm gonna do is i'm just gonna draw something similar here but i'm going to first just divide into six sections and then i'll show the the myelinated fiber so they let the first one be myelinated so i'm gonna just scratch that in give it a little protection.

01:34 The second one is unmylonated, so we'll leave that alone.

01:37 The next two are myelinated, so we'll sheave those accents in myelin, and then the next one is unmyelinated, and then the last one is milanated, so that's what that looks like.

01:50 And so this is partially milanated.

01:57 Fiber c is completely milanated.

02:02 So what this looks like is again we divide it into six sections like so, but everything is myelinated.

02:13 So this is, i'll draw that a little bit better.

02:17 And i'll just make these sections a little bit clearer, a little harder to see them there.

02:22 So there we go.

02:23 So this is fully myelinated.

02:29 Okay.

02:31 So that's what we're dealing with.

02:33 Now, it tells us that for an unmyelinated axon, the nerve signal goes at around 2 meters per second.

02:41 For a myelinated axon, it goes around 25 meters per second.

02:45 Now, what it asks us to do is to draw qualitatively position, accurate position, and velocity time graphs for the nerve impulses.

02:55 So basically, fiber a, so i'll do this in, we'll do fiber a, and then the graph will be x versus t.

03:09 We're just going to use x versus position, and then velocity versus t.

03:15 So we only need a quadrant one graph for these ones, and then time is horizontal, position is vertical.

03:23 For the other graph, velocity will be horizontal, sorry, velocity will be vertical, time will be horizontal.

03:30 So those are quality, you know, those are just basic, basic velocity time graphs.

03:36 Now for fiber a, there's not there's not going to be any change in the velocity.

03:42 So oftentimes i think velocity is the easiest thing to start with because in these types of problems, you're given the most information about velocity.

03:50 Now basically what we know for fiber a is that it's just a constant velocity down every axon.

03:56 Now what i'm going to do is i'm going to kind of divide these these these these these sections into well actually i'll hold off on that for for fiber a it's it's not going to be particularly difficult the velocity is going to be constant all the way down and it's going to be a low velocity it will be just at two and i'll put units up here just so we know meters per second and then time was in seconds and and basically this will have a constant velocity kind of like so.

04:38 Now, so just a standard, low constant velocity at two meters per second.

04:45 Now what this means is that the position time graph will, it will have a constant, it will have a constant velocity the entire time.

04:59 Now, that means position will increase, but the slope will be constant.

05:03 Now i'm going to give that a fairly small slope...

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